The 25-year-old moved to Anfield in January 2013 in a reported £12 million deal from Premier League rivals Chelsea and has become a fans' favourite with the Merseysiders.
Sturridge has scored 37 goals in just 52 appearances since moving to Liverpool and is set for a key role as they look to build on last season's second-placed league finish.
"There are talks ongoing with Daniel Sturridge's representatives," Rodgers said. "[But] there's no more news other than that."
Sturridge has not featured for Liverpool since injuring his thigh while on England duty in the previous international window last month.
Rodgers was critical of England's handing of Sturridge and made it known that he felt he should not be included in Roy Hodgson's latest squad for the Euro 2016 qualifying double header with San Marino and Estonia.
Subsequently, Sturridge was left out of the 21-man party and Rodgers insists there is no lingering issue between himself and Hodgson over the conflict of interest.
"I get on with Roy and spoke with him," he added. "The communication has been good. We agreed it was probably too soon for Daniel Sturridge to meet up with England.
"There is no issue with England. I don't think the same thing will happen again. My focus is on getting Sturridge fit for Liverpool. He has been out for nearly four weeks with a grade one strain."
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